{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "d0655e71",
   "metadata": {},
   "source": [
    "# Project #3\n",
    "## Use Newton method to solve the static operating point of the target circuit"
   ]
  },
  {
   "attachments": {
    "Project_3_Cover.jpg": {
     "image/jpeg": 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    }
   },
   "cell_type": "markdown",
   "id": "66c81ace",
   "metadata": {},
   "source": [
    "![Project_3_Cover.jpg](attachment:Project_3_Cover.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be502c75",
   "metadata": {},
   "source": [
    "### 马梓荃 电子科学与技术 20201060339 979324173@qq.com"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22035ca6",
   "metadata": {},
   "source": [
    "## Step #1 问题分析"
   ]
  },
  {
   "attachments": {
    "Project_3_Problem.jpg": {
     "image/jpeg": 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"
    }
   },
   "cell_type": "markdown",
   "id": "9d1ff667",
   "metadata": {},
   "source": [
    "![Project_3_Problem.jpg](attachment:Project_3_Problem.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3550cb8b",
   "metadata": {},
   "source": [
    "### 由电路图可列方程组如下：\n",
    "$$\n",
    "\\begin{cases}\n",
    "V_1 - V_2 + 11 * V_3 = -55\\\\\n",
    "-V_1 + 12 * V_2 - 11 * V_3 = -11 * I\\\\\n",
    "11 * V_1 - 11 * V_2 + V_3 = 55\\\\\n",
    "I = 10^{-14} * (e^\\frac {V_2} {0.026} - 1)\n",
    "\\end{cases}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8dee64c5",
   "metadata": {},
   "source": [
    "### 对应的函数为:\n",
    "$$\n",
    "f_1(V_1,V_2,V_3)=V_1 - V_2 + 11 * V_3 + 55\\\\\n",
    "f_2(V_1,V_2,V_3)=-V_1 + 12 * V_2 - 11 * V_3 + 11 * I\\\\\n",
    "f_3(V_1,V_2,V_3)=11 * V_1 - 11 * V_2 + V_3 - 55\\\\\n",
    "I = 10^{-14} * (e^\\frac {V_2} {0.026} - 1)\n",
    "$$\n",
    "###### (在这里，为保持美观未将I代入，后续展示也将保持I的存在，在计算时省略代入,展示结果)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9440bc11",
   "metadata": {},
   "source": [
    "### 写出F(X):\n",
    "$$\n",
    "F(V_1,V_2,V_3)=\n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "V_1 - V_2 + 11 * V_3 + 55\\\\\n",
    "-V_1 + 12 * V_2 - 11 * V_3 + 11 * I\\\\\n",
    "11 * V_1 - 11 * V_2 + V_3 - 55\n",
    "\\end{matrix}\n",
    "\\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36a27c45",
   "metadata": {},
   "source": [
    "### 写出DF(X):\n",
    "$$\n",
    "F(V_1,V_2,V_3)=\n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "1 & -1 & 11\\\\\n",
    "-1 & 12+\\frac {11} {26} * 10^{-11} * e^\\frac {V_2} {0.026} & -11\\\\\n",
    "11 & -11 & 1\n",
    "\\end{matrix}\n",
    "\\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb33630d",
   "metadata": {},
   "source": [
    "## Step #2 写出F(X)的Python代码"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "cd367a08",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "e = 2.718281828459\n",
    "def F(v):\n",
    "    f1 = v[0] - v[1] + 11 * v[2] + 55\n",
    "    f2 = -v[0] + 12 * v[1] - 11 * v[2] + 11 * (10 ** -14) * (e ** (v[1]/0.026) - 1)\n",
    "    f3 = 11 * v[0] - 11 * v[1] + v[2] - 55\n",
    "    return np.array([f1,f2,f3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "36578c9b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 8.7000000e+01,  2.8097037e+20, -6.3000000e+01])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = np.array([1,2,3])\n",
    "F(v)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9d11940",
   "metadata": {},
   "source": [
    "## Step #3 写出DF(X)的Python代码"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "91923d4e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def DF(v):\n",
    "    df11 = 1\n",
    "    df12 = -1\n",
    "    df13 = 11\n",
    "    df21 = -1\n",
    "    df22 = 12 + (11 / 26) * (10 ** -11) * (e ** (v[1]/0.026)) \n",
    "    df23 = -11\n",
    "    df31 = 11\n",
    "    df32 = -11\n",
    "    df33 = 1\n",
    "    return np.array([\n",
    "        [df11,df12,df13],\n",
    "        [df21,df22,df23],\n",
    "        [df31,df32,df33]\n",
    "    ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "88e220d4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.00000000e+00, -1.00000000e+00,  1.10000000e+01],\n",
       "       [-1.00000000e+00,  1.08065527e+22, -1.10000000e+01],\n",
       "       [ 1.10000000e+01, -1.10000000e+01,  1.00000000e+00]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = np.array([1,2,3])\n",
    "DF(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "27f8d3b5",
   "metadata": {},
   "outputs": [],
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